We examine the extent to which the response of a perfectly elastic hal
fspace to an SH-wave incident from below can be characterized when kno
wledge about the elastic structure is Limited to the near surface. Ela
stic properties are modeled as piecewise continuous functions of the d
epth coordinate. It is found that the site amplification function can
be determined with a frequency resolution that depends inversely on th
e depth to which the elastic structure is known. Specifically, certain
spectral averages of the site amplification function, concentrated ov
er bandwidth Delta f, depend only on the elastic structure down to a t
wo-way travel-time depth of 1/Delta f. These spectral averages are ent
irely independent of the elastic properties at greater depth. Equivale
ntly, when the incident motion has a bandlimited white power spectrum
of bandwidth Delta f, the site amplification of the root mean square (
rms) ground motion depends only on the elastic structure down to a two
-way travel-time depth of 1/Delta f. When the bandwidth is sufficientl
y large, the following corollary applies: the rms surface ground motio
n equals the rms incident motion multiplied by 2 root I-b/I-0, where I
-0 and I-b are shear impedances at the ground surface and basement dep
th, respectively. This result provides justification for a procedure c
onventionally used to correct stochastic estimates of earthquake groun
d motion to account for local site effects. The analysis also clarifie
s the limitations of that conventional procedure. The results define s
pecific site-response parameters that can be computed from knowledge o
f shallow structure alone and may thereby contribute to improved under
standing of the physical basis for, and limitations of, site classific
ation schemes that are based on average S-wave velocity at shallow dep
th. While the analytical results are rigorous only for infinite Q, num
erical experiments indicate that similar results apply to models with
finite, frequency-independent Q. The practical utility of the results
is likely to be limited primarily by the degree of lateral heterogenei
ty present near sites of interest and the degree to which the sites re
spond nonlinearly to incident ground motion.